As graph models become increasingly prevalent in the processing of scientific data, the exploration of effective methods for the mining of meaningful patterns from large-scale graphs has garnered significant research attention. This paper delves into the complexity of frequent subgraph mining and proposes a frequent subgraph mining (FSM) algorithm. This FSM algorithm is developed within a distributed graph iterative system, designed for the Big Cloud (BC) environment of the China Mobile Corp., and is based on the bulk synchronous parallel (BSP) model, named FSM-BC-BSP. Its aim is to address the challenge of mining frequent subgraphs within a single, large graph. This study advocates for the incorporation of a message sending and receiving mechanism to facilitate data sharing across various stages of the frequent subgraph mining algorithm. Additionally, it suggests employing a standard coded subgraph and sending it to the same node for global support calculation on the large graph. The adoption of the rightmost path expansion strategy in generating candidate subgraphs helps to mitigate the occurrence of redundant subgraphs. The use of standard coding ensures the unique identification of subgraphs, thus eliminating the need for isomorphism calculations. Support calculation is executed using the Minimum Image (MNI) measurement method, aligning with the downward closure attribute. The experimental results demonstrate the robust performance of the FSM-BC-BSP algorithm across diverse input datasets and parameter configurations. Notably, the algorithm exhibits exceptional efficacy, particularly in scenarios with low support requirements, showcasing its superior performance under such conditions.